I came across this forum as I am looking forward to buy a Levante and wanted to know a bit more on your experiences.
Most times, slipping transmissions won't show anything at the mechanic's scanner, still they slip and eventually a major overhaul will be mandatory. Being a premium car and new, I wouldn't set for anything but a complete transmission replacement; not fixed in any way.
I have seen a lot of slipping transmissions in different Audi's (A4, A6 and TT) and dealers always deny it as it implies the complete replacement of the transmission; please notice that nowadays transmissions have a lot of electronics and they don't really have many spare partes to replace and they are so complicated that it takes more shop time than its worth.
The best way to reproduce a slipping transmission is to push it hard along a steep hillclimb; don't do manual changes, let it downshift and change on its own. Find the proper place near the dealer and take him along with the head mechanic for a ride to show them that it is really happening and it must be replaced.